<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>cdfbet</title>
  </head>
  <body bgcolor="#FFFFFF">
    <center>Scilab Function</center>
    <div align="right">Last update : Dec 1997</div>
    <p>
      <b>cdfbet</b> -  cumulative distribution function Beta distribution</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[P,Q]=cdfbet("PQ",X,Y,A,B)  </tt>
      </dd>
      <dd>
        <tt>[X,Y]=cdfbet("XY",A,B,P,Q)  </tt>
      </dd>
      <dd>
        <tt>[A]=cdfbet("A",B,P,Q,X,Y)  </tt>
      </dd>
      <dd>
        <tt>[B]=cdfbet("B",P,Q,X,Y,A)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>P,Q,X,Y,A,B</b>
        </tt>: five real vectors of the same size.</li>
      <li>
        <tt>
          <b>P,Q (Q=1-P)  </b>
        </tt>: The integral from 0 to X of the beta distribution (Input range: [0, 1].)</li>
      <li>
        <tt>
          <b>Q</b>
        </tt>: 1-P</li>
      <li>
        <tt>
          <b>X,Y (Y=1-X)  </b>
        </tt>: Upper limit of integration of beta density (Input range: [0,1],  Search range: [0,1]) A,B : The two parameters of the beta density (input range: (0, +infinity), Search range: [1D-300,1D300] )</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Calculates any one parameter of the beta distribution given
    values for the others (The beta density is proportional to 
    <tt>
        <b>t^(A-1) * (1-t)^(B-1)</b>
      </tt>.</p>
    <p>
    Cumulative distribution function  (P)  is calculated directly by
    code associated with the following reference.</p>
    <p>
    DiDinato, A. R. and Morris,  A.   H.  Algorithm 708: Significant
    Digit Computation of the Incomplete  Beta  Function Ratios.  ACM
    Trans. Math.  Softw. 18 (1993), 360-373.</p>
    <p>
    Computation of other parameters involve a seach for a value that
    produces  the desired  value  of P.   The search relies  on  the
    monotinicity of P with the other parameter.</p>
    <p>
    From DCDFLIB: Library of Fortran Routines for Cumulative Distribution
    Functions, Inverses, and Other Parameters (February, 1994)
    Barry W. Brown, James Lovato and Kathy Russell. The University of
    Texas.</p>
  </body>
</html>
